In a medium sauce pan, place chicken, half the celery, half the onion, parsley and cover with water.Add bullion and cook on medium flame, covered for about 15-20 minutes, until chicken is cooked through.Once cooked, remove chicken and let cool. Reserve chicken broth.Cut chicken into small pieces and place in a bowl. Add onions, celery and mayonnaise, 1/8 cup reserved chicken broth and mix well. If looks dry add 1/8 cup more.Serve on a bed of lettuce, in a lettuce wrap or on your favorite bread.